The integrals converge. Evaluate the integrals without using tables \int_{0}^{1}\frac{4rdr}{\sqrt{1-r^{4}}}

Armorikam 2020-10-26 Answered
The integrals converge. Evaluate the integrals without using tables
014rdr1r4
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2abehn
Answered 2020-10-27 Author has 88 answers
Step 1: Given that
The integrals converge. Evaluate the integrals without using tables
014rdr1r4
Step 2: Solve
We have,
014rdr1r4dr=014r1(r2)2dr
Substitute,
r2=t
2r.dr=dt
dr=dt2r
Plugging all the values into the integral we obtain,
014r1(r2)2dr014r1t2×dt2r
=201dt1t2
=2[sin1(t)]01
=2(sin1(1)0)
=2sin1sin(π2)
=2×π2
=π
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Jeffrey Jordon
Answered 2021-11-08 Author has 2087 answers

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